WASHINGTON — Reacting to the release of a video Tuesday showing the execution of a second U.S. hostage, journalist Steven Sotloff, by the extremist Islamic State of Iraq & Al-Sham, U.S. lawmakers are calling on President Barack Obama to expand the U.S.’s military role in the Middle East.

They are urging Mr. Obama to step up efforts to forge a broad coalition of nations that would take on ISIS in both Iraq and Syria. The U.S. president said last week he planned to send John Kerry, the U.S. secretary of state, to the Mideast to seek support from nations in the region.

“There is a growing awareness internationally that we have to form an unprecedented international program of cooperation,” said Representative Ed Royce of California, the Republican chairman of the House Foreign Affairs Committee, echoing calls from such hawks as U.S. senators Lindsay Graham and Bill Nelson on the weekend.

But some Obama administration officials said they and the president are wary of expanding the overt U.S. military role.

Doing so risks unwittingly assisting the extremists’ efforts to define the conflict as part of a centuries-old Christian crusader and Jewish war against Islam, according to six officials who asked for anonymity to discuss internal policy deliberations.

While Mr. Obama has authorized limited airstrikes against ISIS in Iraq for humanitarian purposes and to protect U.S. personnel, he said last week “we don’t have a strategy yet” to extend the fight into Syria.

The U.S. backs what it calls moderate rebels seeking to overthrow Syria’s President Bashar Al-Assad, even as ISIS has made greater headway against his forces.

In Tuesday’s video, a man brandishing a knife warns Mr. Obama as long as U.S. airstrikes against the militant group continue, “our knife will continue to strike the necks of your people.”

The footage — depicting what the U.S. called a sickening act of brutality — was posted two weeks after the release of video showing the killing of James Foley and just days after Mr. Sotloff’s mother pleaded for his life.

David Cameron, the British Prime Minister, said he would chair an emergency response meeting with his Cabinet Wednesday to review the latest developments.

In Washington, State Department spokeswoman Jen Psaki said U.S. intelligence analysts will work as quickly as possible to determine if the video is authentic.

“If the video is genuine, we are sickened by this brutal act, taking the life of another innocent American citizen,” she said. “Our hearts go out to the Sotloff family.”

Ms. Psaki said it is believed “a few” Americans are still being held by ISIS. She would not give any specifics, but one is a 26-year-old woman kidnapped while doing humanitarian aid work in Syria, said a family representative who asked the hostage not be identified out of fear for her safety.

The fighter who apparently beheads Mr. Sotloff in the video calls it retribution for Mr. Obama’s continued airstrikes against the group.

“I’m back, Obama, and I’m back because of your arrogant foreign policy toward the Islamic State … despite our serious warnings,” the fighter says. “So just as your missiles continue to strike our people, our knife will continue to strike the necks of your people.”

He mentions the recent U.S. airstrikes around the Mosul dam and the beleaguered Iraqi town of Amerli, making it unlikely Mr. Sotloff was killed at the same time as Mr. Foley, as some analysts had speculated.

On the weekend, Iraqi government forces with help from U.S. airstrikes broke ISIS’s two-month siege of Amerli, a town where 15,000 Shiite Turkmen had been stranded.

The SITE Intelligence Group, a U.S. terrorism watchdog, first reported the video’s existence.

In a sign of disorganization — or perhaps dissension — in the extremist group’s ranks, an ISIS faction posted the video early, before it was supposed to be released. In a later Twitter message, those responsible apologized and asked fellow jihadis not to “reproach” them.

Last week, Mr. Sotloff’s mother, Shirley, pleaded with his captors, saying in a video her son was “an innocent journalist” and “an honourable man” who “has always tried to help the weak.”

Mr. Sotloff grew up in the Miami area, graduated from Kimball Union Academy, a prep school in New Hampshire, then attended the University of Central Florida, where he majored in journalism but apparently left without graduating.

Just how he made his way from Florida to Middle East hot spots is not clear. He published articles from Syria, Egypt and Libya in several publications, many focusing on the plight of ordinary people in war-torn places.

At Mr. Sotloff’s parents’ home in Pinecrest, Fla., two police vehicles blocked the driveway Tuesday, and officers advised journalists to stay away.